{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import random\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.animation as animation\n",
    "from IPython.display import HTML"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3, 4, 5, 6, 7, 8, 9]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shape = list(range(1,10))\n",
    "shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  2,  3,  4,  5,  6,  7,  8,  9],\n",
       "       [10, 11, 12, 13, 14, 15, 16, 17, 18],\n",
       "       [19, 20, 21, 22, 23, 24, 25, 26, 27],\n",
       "       [28, 29, 30, 31, 32, 33, 34, 35, 36]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "row, column = random.choice(shape), random.choice(shape)\n",
    "matrix = np.array([n for n in range(1,row*column+1)]).reshape(row,column) \n",
    "matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.imshow(matrix, cmap='gray', vmin=0, vmax=1)\n",
    "for (i, j), val in np.ndenumerate(matrix):\n",
    "    ax.text(j, i, val, ha='center', va='center', color='black')\n",
    "#隐藏坐标   \n",
    "ax.set_xticks([])\n",
    "ax.set_yticks([])\n",
    "#内部线\n",
    "ax.set_xticks(np.arange(-.5, matrix.shape[1], 1), minor=True)\n",
    "ax.set_yticks(np.arange(-.5, matrix.shape[0], 1), minor=True)\n",
    "ax.grid(which=\"minor\", color=\"black\", linestyle='-', linewidth=2)\n",
    "ax.tick_params(which=\"minor\", size=0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def algorithm(matrix):\n",
    "    rows, columns = len(matrix), len(matrix[0])   #行、列数\n",
    "    nums = [0]*rows*columns                       #输出向量初始化\n",
    "    start_x, start_y = 0,0                        #指针初始位置——x代表行，y代表列\n",
    "    loop= (min(rows, columns)+1)//2               #指针转圈数\n",
    "    count = 0                                     #索引计数器\n",
    "    \n",
    "    move = []             #中间移动索引列表\n",
    "    \n",
    "    for offset in range(0, loop):\n",
    "        if rows-offset-start_x == 1 and columns-offset-start_y == 1:      #1*1矩阵以及方阵的中心元素\n",
    "            nums[count] = matrix[start_x][start_y]\n",
    "            move.append((start_x,start_y))\n",
    "        elif rows-offset-start_x == 1:                                    #列数大于行数矩阵最核心一行\n",
    "            for j in range(start_y, columns-offset):\n",
    "                nums[count] = matrix[start_x][j]\n",
    "                count +=1\n",
    "                move.append((start_x,j))\n",
    "        elif columns-offset-start_y == 1:                                         #列数小于行数矩阵最核心一列\n",
    "            for i in range(start_x, rows-offset):\n",
    "                nums[count] = matrix[i][start_y]\n",
    "                count +=1\n",
    "                move.append((i,start_y))\n",
    "                \n",
    "        else:                                                             #外围完整循环层\n",
    "            for j in range(start_y, columns-offset-1):                    #不含该行最后一个元素，该元素作为下一列的开头\n",
    "                nums[count] = matrix[start_x][j]\n",
    "                count +=1\n",
    "                move.append((start_x,j))\n",
    "            for i in range(start_x, rows-offset-1):                       #不含该列最后一个元素，该元素作为下一行的开头\n",
    "                nums[count] = matrix[i][columns-offset-1]\n",
    "                count +=1\n",
    "                move.append((i,columns-offset-1))\n",
    "            for j in range(columns-offset-1, start_y, -1):\n",
    "                nums[count] = matrix[rows-offset-1][j]\n",
    "                count +=1\n",
    "                move.append((rows-offset-1,j))\n",
    "            for i in range(rows-offset-1, start_x, -1):\n",
    "                nums[count] = matrix[i][start_y]  \n",
    "                count +=1\n",
    "                move.append((i,start_y))\n",
    "            start_x +=1\n",
    "            start_y +=1\n",
    "\n",
    "    return move, nums"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1,\n",
       " 2,\n",
       " 3,\n",
       " 4,\n",
       " 5,\n",
       " 6,\n",
       " 7,\n",
       " 8,\n",
       " 9,\n",
       " 18,\n",
       " 27,\n",
       " 36,\n",
       " 35,\n",
       " 34,\n",
       " 33,\n",
       " 32,\n",
       " 31,\n",
       " 30,\n",
       " 29,\n",
       " 28,\n",
       " 19,\n",
       " 10,\n",
       " 11,\n",
       " 12,\n",
       " 13,\n",
       " 14,\n",
       " 15,\n",
       " 16,\n",
       " 17,\n",
       " 26,\n",
       " 25,\n",
       " 24,\n",
       " 23,\n",
       " 22,\n",
       " 21,\n",
       " 20]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "move, nums = algorithm(matrix)\n",
    "nums"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<link rel=\"stylesheet\"\n",
       "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/css/font-awesome.min.css\">\n",
       "<script language=\"javascript\">\n",
       "  function isInternetExplorer() {\n",
       "    ua = navigator.userAgent;\n",
       "    /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
       "    return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
       "  }\n",
       "\n",
       "  /* Define the Animation class */\n",
       "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
       "    this.img_id = img_id;\n",
       "    this.slider_id = slider_id;\n",
       "    this.loop_select_id = loop_select_id;\n",
       "    this.interval = interval;\n",
       "    this.current_frame = 0;\n",
       "    this.direction = 0;\n",
       "    this.timer = null;\n",
       "    this.frames = new Array(frames.length);\n",
       "\n",
       "    for (var i=0; i<frames.length; i++)\n",
       "    {\n",
       "     this.frames[i] = new Image();\n",
       "     this.frames[i].src = frames[i];\n",
       "    }\n",
       "    var slider = document.getElementById(this.slider_id);\n",
       "    slider.max = this.frames.length - 1;\n",
       "    if (isInternetExplorer()) {\n",
       "        // switch from oninput to onchange because IE <= 11 does not conform\n",
       "        // with W3C specification. It ignores oninput and onchange behaves\n",
       "        // like oninput. In contrast, Mircosoft Edge behaves correctly.\n",
       "        slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
       "        slider.setAttribute('oninput', null);\n",
       "    }\n",
       "    this.set_frame(this.current_frame);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.get_loop_state = function(){\n",
       "    var button_group = document[this.loop_select_id].state;\n",
       "    for (var i = 0; i < button_group.length; i++) {\n",
       "        var button = button_group[i];\n",
       "        if (button.checked) {\n",
       "            return button.value;\n",
       "        }\n",
       "    }\n",
       "    return undefined;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.set_frame = function(frame){\n",
       "    this.current_frame = frame;\n",
       "    document.getElementById(this.img_id).src =\n",
       "            this.frames[this.current_frame].src;\n",
       "    document.getElementById(this.slider_id).value = this.current_frame;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.next_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.previous_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.first_frame = function()\n",
       "  {\n",
       "    this.set_frame(0);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.last_frame = function()\n",
       "  {\n",
       "    this.set_frame(this.frames.length - 1);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.slower = function()\n",
       "  {\n",
       "    this.interval /= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.faster = function()\n",
       "  {\n",
       "    this.interval *= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_forward = function()\n",
       "  {\n",
       "    this.current_frame += 1;\n",
       "    if(this.current_frame < this.frames.length){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.first_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.last_frame();\n",
       "        this.reverse_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.last_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_reverse = function()\n",
       "  {\n",
       "    this.current_frame -= 1;\n",
       "    if(this.current_frame >= 0){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.last_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.first_frame();\n",
       "        this.play_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.first_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.pause_animation = function()\n",
       "  {\n",
       "    this.direction = 0;\n",
       "    if (this.timer){\n",
       "      clearInterval(this.timer);\n",
       "      this.timer = null;\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.play_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = 1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_forward();\n",
       "    }, this.interval);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.reverse_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = -1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_reverse();\n",
       "    }, this.interval);\n",
       "  }\n",
       "</script>\n",
       "\n",
       "<style>\n",
       ".animation {\n",
       "    display: inline-block;\n",
       "    text-align: center;\n",
       "}\n",
       "input[type=range].anim-slider {\n",
       "    width: 374px;\n",
       "    margin-left: auto;\n",
       "    margin-right: auto;\n",
       "}\n",
       ".anim-buttons {\n",
       "    margin: 8px 0px;\n",
       "}\n",
       ".anim-buttons button {\n",
       "    padding: 0;\n",
       "    width: 36px;\n",
       "}\n",
       ".anim-state label {\n",
       "    margin-right: 8px;\n",
       "}\n",
       ".anim-state input {\n",
       "    margin: 0;\n",
       "    vertical-align: middle;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<div class=\"animation\">\n",
       "  <img id=\"_anim_img2388bcd998bc4adbbece0eafa1bc0acd\">\n",
       "  <div class=\"anim-controls\">\n",
       "    <input id=\"_anim_slider2388bcd998bc4adbbece0eafa1bc0acd\" type=\"range\" class=\"anim-slider\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           oninput=\"anim2388bcd998bc4adbbece0eafa1bc0acd.set_frame(parseInt(this.value));\"></input>\n",
       "    <div class=\"anim-buttons\">\n",
       "      <button title=\"Decrease speed\" onclick=\"anim2388bcd998bc4adbbece0eafa1bc0acd.slower()\">\n",
       "          <i class=\"fa fa-minus\"></i></button>\n",
       "      <button title=\"First frame\" onclick=\"anim2388bcd998bc4adbbece0eafa1bc0acd.first_frame()\">\n",
       "        <i class=\"fa fa-fast-backward\"></i></button>\n",
       "      <button title=\"Previous frame\" onclick=\"anim2388bcd998bc4adbbece0eafa1bc0acd.previous_frame()\">\n",
       "          <i class=\"fa fa-step-backward\"></i></button>\n",
       "      <button title=\"Play backwards\" onclick=\"anim2388bcd998bc4adbbece0eafa1bc0acd.reverse_animation()\">\n",
       "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "      <button title=\"Pause\" onclick=\"anim2388bcd998bc4adbbece0eafa1bc0acd.pause_animation()\">\n",
       "          <i class=\"fa fa-pause\"></i></button>\n",
       "      <button title=\"Play\" onclick=\"anim2388bcd998bc4adbbece0eafa1bc0acd.play_animation()\">\n",
       "          <i class=\"fa fa-play\"></i></button>\n",
       "      <button title=\"Next frame\" onclick=\"anim2388bcd998bc4adbbece0eafa1bc0acd.next_frame()\">\n",
       "          <i class=\"fa fa-step-forward\"></i></button>\n",
       "      <button title=\"Last frame\" onclick=\"anim2388bcd998bc4adbbece0eafa1bc0acd.last_frame()\">\n",
       "          <i class=\"fa fa-fast-forward\"></i></button>\n",
       "      <button title=\"Increase speed\" onclick=\"anim2388bcd998bc4adbbece0eafa1bc0acd.faster()\">\n",
       "          <i class=\"fa fa-plus\"></i></button>\n",
       "    </div>\n",
       "    <form title=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_select2388bcd998bc4adbbece0eafa1bc0acd\"\n",
       "          class=\"anim-state\">\n",
       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_2388bcd998bc4adbbece0eafa1bc0acd\"\n",
       "             >\n",
       "      <label for=\"_anim_radio1_2388bcd998bc4adbbece0eafa1bc0acd\">Once</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_2388bcd998bc4adbbece0eafa1bc0acd\"\n",
       "             checked>\n",
       "      <label for=\"_anim_radio2_2388bcd998bc4adbbece0eafa1bc0acd\">Loop</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_2388bcd998bc4adbbece0eafa1bc0acd\"\n",
       "             >\n",
       "      <label for=\"_anim_radio3_2388bcd998bc4adbbece0eafa1bc0acd\">Reflect</label>\n",
       "    </form>\n",
       "  </div>\n",
       "</div>\n",
       "\n",
       "\n",
       "<script language=\"javascript\">\n",
       "  /* Instantiate the Animation class. */\n",
       "  /* The IDs given should match those used in the template above. */\n",
       "  (function() {\n",
       "    var img_id = \"_anim_img2388bcd998bc4adbbece0eafa1bc0acd\";\n",
       "    var slider_id = \"_anim_slider2388bcd998bc4adbbece0eafa1bc0acd\";\n",
       "    var loop_select_id = \"_anim_loop_select2388bcd998bc4adbbece0eafa1bc0acd\";\n",
       "    var frames = new Array(36);\n",
       "    \n",
       "  frames[0] = \"\\\n",
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    "marker, = ax.plot([], [], marker=\"o\", color=\"blue\", markersize=30)\n",
    "\n",
    "def update(idx):\n",
    "    marker.set_data(idx[1], idx[0])\n",
    "    return marker,\n",
    "\n",
    "ani = animation.FuncAnimation(fig, update, frames=move, interval=1000, blit=True)\n",
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